Elliptic curve isogeny class with Cremona label 50400dg (LMFDB label 50400.br)

• Label: 50400dg
• Number of curves: $4$
• Conductor: $50400$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 50400dg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 50400dg do not have complex multiplication.

Modular form 50400.2.a.dg

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 50400dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
50400.br3	50400dg1	\([0, 0, 0, -15825, 754000]\)	\(601211584/11025\)	\(8037225000000\)	\([2, 2]\)	\(147456\)	\(1.2710\)	\(\Gamma_0(N)\)-optimal
50400.br4	50400dg2	\([0, 0, 0, -75, 2187250]\)	\(-8/354375\)	\(-2066715000000000\)	\([2]\)	\(294912\)	\(1.6176\)
50400.br2	50400dg3	\([0, 0, 0, -32700, -1136000]\)	\(82881856/36015\)	\(1680315840000000\)	\([2]\)	\(294912\)	\(1.6176\)
50400.br1	50400dg4	\([0, 0, 0, -252075, 48712750]\)	\(303735479048/105\)	\(612360000000\)	\([4]\)	\(294912\)	\(1.6176\)